Answer: the lengths are 20 feet, 23 feet and 37 feet
Step-by-step explanation:
Let x represent the length of the shorter side of the triangular deck.
The second side of a triangular deck is 3 feet longer than the shortest side. This means that the length of the second side is (x + 3) feet.
The third side is 3 feet shorter than twice the length of the shortest side. This means that the length of the third of the triangle is (2x - 3) feet.
If the perimeter of the deck is 80 feet, it means that
x + x + 3 + 2x - 3 = 80
4x = 80
x = 80/4
x = 20
The length of the second side is
20 + 3 = 23 feet
The length of the third side is
20 × 2 - 3 = 40 - 3 = 37 feet
